Problem: The sum of two numbers is $112$, and their difference is $86$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 112}$ ${x-y = 86}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 198 $ $ x = \dfrac{198}{2} $ ${x = 99}$ Now that you know ${x = 99}$ , plug it back into $ {x+y = 112}$ to find $y$ ${(99)}{ + y = 112}$ ${y = 13}$ You can also plug ${x = 99}$ into $ {x-y = 86}$ and get the same answer for $y$ ${(99)}{ - y = 86}$ ${y = 13}$ Therefore, the larger number is $99$, and the smaller number is $13$.